The distribution of L (K) revealed a continuously increasing curve without a clear maximum for true K. To overcome these difficulties in identifying the true K value, an ad hoc quantity (ΔK) was calculated based on the second-order rate of change of likelihood (∆K) using the software Structure Harvest (Evanno et al. 2005; Earl 2012).
According to the ad hoc quantity ∆ K [ 37], the most likely number of clusters was three (Additional file 8: Figure S4).
This test uses an ad hoc quantity (delta K) calculated based on the second order rate of change of the likelihood (delta K).
In order to overcome the difficulty in interpreting which the real value of K would be, another ad hoc quantity (Δ K) was used.
The second method, developed by Evanno et al. [ 48] finds the ad hoc quantity based on the second order rate of change of the likelihood function with respect to K (Δ K).
Daily at noon following husbandry, we placed a bowl (18 cm diameter, 4 cm deep) containing 100 g of crumb (ad libitum quantity) and 200 g of sand into each cage, alternating on which side of the central divider the bowl was positioned.
The ad hoc quantity based on the second order rate of change of the likelihood function (ΔK) [ 46] revealed a first level of clustering at K = 2 for the investigated Mediterranean apricots (ΔK = 61.81; Figure 3; see Additional file 4: Figure S1) and a sub-clustering at K = 4 (ΔK = 3.6).
The model choice criterion to detect the most probable value of K was Δ K, an ad hoc quantity related to the second order change of the log probability of data with respect to the number of clusters inferred by Structure [ 29].
Δ K, an ad hoc quantity related to the second order change of the log probability of data with respect to the number of clusters inferred by the Structure program, proved an useful method for identifying a more probably true value of K when there was no previous model or a pre-defined number of groups to rely on.
In this period of occupation and during the numerous wars fought between Rome and the Germans in the 1st century ad, enormous quantities of information about the Germans reached Rome, and, when Tacitus published in ad 98 the book now known as the Germania, he had reliable sources of information on which to draw.
